{
  "id": "0902.2217",
  "version": "v1",
  "published": "2009-02-12T21:03:31.000Z",
  "updated": "2009-02-12T21:03:31.000Z",
  "title": "The ring of regular functions of an algebraic monoid",
  "authors": [
    "Lex E. Renner",
    "Alvaro Rittatore"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let M be an irreducible normal algebraic monoid with unit group G. It is known that G admits a Rosenlicht decomposition, G=G_antG_aff, where G_ant is the maximal anti-affine subgroup of G, and G_aff the maximal normal connected affine subgroup of G. In this paper we show that this decomposition extends to a decomposition M=G_antM_aff, where M_aff is the affine submonoid M_aff=\\bar{G_aff}. We then use this decomposition to calculate $\\mathcal{O}(M)$ in terms of $\\mathcal{O}(M_aff)$ and G_aff, G_ant\\subset G. In particular, we determine when M is an anti-affine monoid, that is when $\\mathcal{O}(M)=K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-12T21:03:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L30"
    ],
    "keywords": [
      "regular functions",
      "maximal normal connected affine subgroup",
      "maximal anti-affine subgroup",
      "irreducible normal algebraic monoid",
      "decomposition extends"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.2217R"
    }
  }
}